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The Grey Cells - Exercise !
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Northman View Drop Down
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Topic: The Grey Cells - Exercise !
    Posted: 30-Sep-2006 at 06:17
You have a PM Giannis !
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Posts: 493 		  Quote Giannis Quote  Post ReplyReply Direct Link To This Post Posted: 01-Oct-2006 at 05:45
Ok, Northman found it as well as Neoptolemos the right answer is the following as Northman PM it to me:
 
 answered by memory and realized my answer was only valid with 4 pirates left.

I looked for the notes I made previously - and with a few changes, here they are, and to explain the logic, I'll start with  only A and B left.

Left 2 pirates (A/B) = A gets 100 coins

Left 3 pirates (A/B/C) =  C can propose 99 to himself and 1 coin to B (B&C=majority)

Left 4 pirates(A/B/C/D) = D can propose 98 coins to himself and 1 coin to each of A and B. A and B will have less if they dont accept - (Majority 3:1)

Wirh all 5 pirates A/B/C/D/E the logic is...

E can propose 2 coins for pirate A (or B), and 1 coin for C and have 97 for himself. He needs to spend an extra coin to one pirate to be sure that this pirate would prefer this proposal instead of what could be proposed with 4 pirates left.
Give me a place to stand and I will move the world.
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 01-Oct-2006 at 09:25
You were first Neo Thumbs Up - your call!
 
 
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Posts: 659 		  Quote Neoptolemos Quote  Post ReplyReply Direct Link To This Post Posted: 01-Oct-2006 at 20:42
The two barbarian pirates that walked away empty-handed, mister B and mister D, are very disappointed about the deal and upset with their fellow pirates. They appeal to the captain, but he tells them that he can't do anything. Our friends, blinded by their anger, decide to quit the pirate career and become (semi-barbarian) thiefs instead.

Six months later they carry out a bank robbery, the security guard tries to chase them, so they shoot at him and manage to get away. Or so they thought... two days later the get arrested by the police!
The police have insufficient evidence for a conviction, but they have enough evidence for their unlawful activity during the last six months. So the police interrogator does the following:
He separates the two suspects, visits each of them and offers the same deal: if one confesses and testifies against the other and the other remains silent, the betrayer will go free and the silent will receive a 10-year prison sentence. If none of them confesses, they will be both sentenced to 1 year in jail for minor charges. If both of them confess, each will receive a 5-year sentence.

Therefore the question is: what are Mr B and Mr D going to do, given that each one wants to minimize his jail term?

PM!
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 03-Oct-2006 at 11:49
Hmmm Neo - I believe there is more than one outcome here.
But I'll give it some more thoughts on my vacation 4.-27. october. Smile
 
But I understand you right in saying - they have no chance to consult one another?
If they, on the other hand do, is it ok for them to cheat the other?
 
 
 
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Posts: 659 		  Quote Neoptolemos Quote  Post ReplyReply Direct Link To This Post Posted: 03-Oct-2006 at 17:08
In such "games" you can never be sure about the outcome, because you can't get into the criminals brain. However, if both of them are rational, there is only one outcome.

You understood right; they can't consult each other. But even if they could see each other for 5 mins, they would still have to return to their rooms to answer to the interrogator's questions and cheating could definately be one of their strategies.
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Posts: 659 		  Quote Neoptolemos Quote  Post ReplyReply Direct Link To This Post Posted: 12-Oct-2006 at 01:21
Nobody found the solution yet???

C'mon it's not hard...
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 22-Jan-2007 at 16:58
Obviously too hard Neo...  I couldnt come up with anything sensible to that one in October - and not now either. Cry
 
Here is an easier one.... everyone can enjoy a little brainwork with this:
 
If 27 frogs can catch 27 flies in 27 minutes, how many frogs are needed to catch 81 flies in 81 minutes?
 
 
 
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Therefore the question is: what are Mr B and Mr D going to do, given that each one wants to minimize his jail term?

That's an easy question relating to the Nash Equilibrium concept in game theory economics.

The scenarios are as follows:

If A confesses:
--If B is silent, then A gets 0 years, B gets 10 years
--If B confesses, then A gets 5 years, B gets 5 years

If A is silent:
-If B is silent, the A gets 1 year, B gets 1 year
-If B confesses, A gets 10 years, B gets 0 years

B will always confess because for any of the two possibilities that A will chose, B will be better off confessing. The same goes for A, who will also confess (you can see this by switching A and B in the chart).

Therefore, the Nash Equilibrium is that both will confess, despite the fact that they would both be better off if they both remain silent. But since they cannot trust one another, the expected outcome is better for each person individually to confess. This is the same reason why two nations engage in arms races even though each know that they will be better off not building up weapons, provided that it is certain that the other does not.


Edited by Imperator Invictus - 22-Jan-2007 at 18:24
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Posts: 3151 		  Quote Imperator Invictus Quote  Post ReplyReply Direct Link To This Post Posted: 22-Jan-2007 at 18:56
If 27 frogs can catch 27 flies in 27 minutes, how many frogs are needed to catch 81 flies in 81 minutes?

27

One approach is to rewrite the question as:
27 frogs are capable of catching 27 files / 27 minutes

In the expression above 27 files / 27 minutes simplifies to 1 fly / 1 minute,
Therefore, 27 frogs are capable of catching 1 fly / 1 minute

The question asks you how many are needed to catch 81 flies in 81 minute, which is 81 flies / 81 minutes = 1 fly / 1 minute. Therefore, the answer is 27 flies because the flies per minute criteria is exactly the same.
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Posts: 659 		  Quote Neoptolemos Quote  Post ReplyReply Direct Link To This Post Posted: 23-Jan-2007 at 01:12
The Grey Cells - resurrected! Big%20smile

Originally posted by Imperator Invictus


Therefore, the Nash Equilibrium is that both will confess, despite the fact that they would both be better off if they both remain silent. But since they cannot trust one another, the expected outcome is better for each person individually to confess. This is the same reason why two nations engage in arms races even though each know that they will be better off not building up weapons, provided that it is certain that the other does not.
Precisely!
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 23-Jan-2007 at 04:58
Well done Invictus - your turn to ask now Thumbs%20Up
 
 
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Posts: 3151 		  Quote Imperator Invictus Quote  Post ReplyReply Direct Link To This Post Posted: 23-Jan-2007 at 20:24
A fishing boat is lying in the harbor. There is a rope ladder hanging over the side with its end touching the water. The rungs of the ladder are 1 meter apart and the tide is rising at 50 centimeters an hour.

At the end of 6 hours, how many of the rungs will be covered?
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Posts: 478 		  Quote Timotheus Quote  Post ReplyReply Direct Link To This Post Posted: 23-Jan-2007 at 20:45
None of the rungs will be covered. The boat will rise with the tide.
Opium is the religion of the masses.

From each according to his need, to each according to his ability.
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That's right! Wink
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Posts: 478 		  Quote Timotheus Quote  Post ReplyReply Direct Link To This Post Posted: 24-Jan-2007 at 00:57
Do I post something now? Gah, let's see if I can think of anything...
Opium is the religion of the masses.

From each according to his need, to each according to his ability.
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 29-Jan-2007 at 19:08
Originally posted by Timotheus

Do I post something now? Gah, let's see if I can think of anything...
 
 
Still thinking Timotheus? Wink
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Posts: 0 		  Quote Hugin Quote  Post ReplyReply Direct Link To This Post Posted: 30-Jan-2007 at 13:23
I think he is Sleepy
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Posts: 4262 		  Quote Northman Quote  Post ReplyReply Direct Link To This Post Posted: 22-Jul-2008 at 15:08
Timotheus might keep himself some long vacations - so lets help him a bit with a story from the early days on All Empires...
 
In the first week we had less than a dozen members.
The next week we got three new members and every week since then, we got two members more than what we got the previous week.
At a certain time, we were 54 members and until then, no members left AE. 
 
How many members did we have to start with?
 
 
 
 
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Posts: 8595 		  Quote Seko Quote  Post ReplyReply Direct Link To This Post Posted: 22-Jul-2008 at 15:22
Oh lordy? A grey cell test! Good idea to re-invigorate this thread.
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